Nonlinear dynamic simulation of hypoid gearbox with elastic housing

A methodology to predict the nonlinear dynamic response of hypoid gearboxes with elastic housing structure is proposed. The dynamic substructure strategy is applied to assemble the hypoid gear pair, shaft-bearing assembly and elastic housing models. The pinion and gear are modeled as rigid bodies with backlash nonlinearity and time-varying mesh coupling. The kinematic transmission error is assumed to be the excitation. The shaft-bearing assemblies are condensed using the finite element technique as stiffness matrices to support the pinion and gear. A lumped parameter representation of the elastic housing is established by applying the modal parameters extracted from an appropriate set of frequency response functions. In order to obtain the rotational coordinates, a rigid body interpolation of the translational responses at the bearing locations on the housing structure is applied. To demonstrate the salient features of the proposed methodology, a practical application is studied to analyze the effect of housing flexibility on the dynamic mesh force, and the effect of external excitation exerted on the housing on the dynamic mesh force and housing surface vibration. The parametric analysis reveals the sensitivity of dynamic mesh force to housing flexibility. Finally, the effect of external force exerted on the housing on gear dynamic responses can be significant and also appears to be location dependent.